English

Adversary Lower Bounds for the Collision and the Set Equality Problems

Quantum Physics 2017-07-31 v4

Abstract

We prove tight Ω(n1/3)\Omega(n^{1/3}) lower bounds on the quantum query complexity of the Collision and the Set Equality problems, provided that the size of the alphabet is large enough. We do this using the negative-weight adversary method. Thus, we reprove the result by Aaronson and Shi, as well as a more recent development by Zhandry.

Cite

@article{arxiv.1310.5185,
  title  = {Adversary Lower Bounds for the Collision and the Set Equality Problems},
  author = {Aleksandrs Belovs and Ansis Rosmanis},
  journal= {arXiv preprint arXiv:1310.5185},
  year   = {2017}
}

Comments

24 pages, 2 figures. v2: rewritten paper, v3: minor typos fixed, v4: simplified proofs

R2 v1 2026-06-22T01:50:02.386Z